# MAFS.3.NF.1.3

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
1. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
2. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
3. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
4. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
General Information
Subject Area: Mathematics
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Develop understanding of fractions as numbers. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Denominators are limited to 2, 3, 4, 6, and 8. Fractions must reference the same whole entity that can be equally partitioned, unless item is assessing MAFS.3.NF.1.3d. Items may not use the term “simplify” or “lowest terms” in directives. Visual models may include number lines and area models. Only whole number marks may be labeled on number lines.
• Calculator :

No

• Context :

Allowable

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

For MAFS.3.NF.1.3c:

Select all the fractions that are equivalent to a whole number.

• Difficulty: N/A
• Type: MS: Multiselect

## Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5020100: STEM Lab Grade 3 (Specifically in versions: 2016 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.3.NF.1.AP.3a: Identify equivalent fractions on a number line divided into fourths and halves within 3 units.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessments

Sample 4 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Sample 3 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Sample 2 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Sample 1 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

## Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

## Formative Assessments

Four Fourths:

Students are given a number line scaled by fourths and ask to label the notches.

Type: Formative Assessment

Generating Equivalent Fractions:

Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.

Type: Formative Assessment

How Many Fourths Are In Two Wholes?:

Students are asked to divide two rectangles into fourths and then to consider how many fourths the two wholes represent.

Type: Formative Assessment

Comparing Fractions:

Students compare two pairs of fractions and record their comparisons using the less than or greater than symbols.

Type: Formative Assessment

The Cake Problem:

Students compare two fractional parts of two different wholes.

Type: Formative Assessment

Equivalent Fractions:

Students determine whether or not fractions are equivalent.

Type: Formative Assessment

## Image/Photograph

Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

## Lesson Plans

The Pizza Exchange:

The students will receive paper pizzas that are divided into different fractional parts. They will decorate their pizza, and then make equal trades with classmates to explore equivalence of fractions. The students will be able to explain equivalence of fractions based on their pizza exchanges and will be able to compare and order the fractional parts by their size.

Type: Lesson Plan

Discovering Fractions:

In this lesson students will make initial discoveries about fractions. Students will work together to explain and record the discoveries they make while using manipulatives to explore fractions.

Type: Lesson Plan

Would You Rather?:

This lesson is designed to help students generate rules for comparing fractions. The students will use fraction tiles to discover ways to compare fractions with the same denominator or fractions with the same numerator. They will also begin to use benchmark fractions to help make comparisons and complete inequalities.

Type: Lesson Plan

Would you rather have?:

Would you rather have 2/4 or 6/12 of a Hershey Chocolate Bar? The students will create a fraction tool kit from construction paper to investigate equivalent fractions using rectangular area models.

Type: Lesson Plan

Who has more? Using the size of the fractional part to compare.:

Students explore how they can compare fractions by considering the denominator. Students use real world examples to create models and demonstrate that the size of the piece decreases as the denominator increases.

Type: Lesson Plan

Match My Fraction:

The students will use pattern blocks to demonstrate fractions and equivalent fractions. They begin by finding and modeling equivalent fractions with pattern blocks, then they are asked to match cards to show the equivalent fractions.

Type: Lesson Plan

Cooking with Fractions:

In this lesson, students will examine real-world recipes and determine if the fractions are less than one or greater than one. Fractions and ingredients are recorded on a chart within the groups. Games are mixed in to make learning interactive and engaging.

Type: Lesson Plan

Comparing Fractions with Pizza:

In this lesson, students will demonstrate their understanding of comparing fractions with the same denominator through engaging problem solving with real-world application to pizza using a model. Students will be actively engaged in a Fraction War game and Would You Rather Have statements to solidify their understanding of comparing fractions with the same denominator.

Type: Lesson Plan

Comparing Fractions with Brownies:

Students will demonstrate their understanding of comparing fractions with the same numerator through engaging problem solving using real-world application with brownies as a model. Students will be actively engaged in a fraction war game and "would you rather have" statements to solidify their understanding of comparing fractions with the same numerator.

Type: Lesson Plan

Fractions on a Number line:

In this lesson, students will have experiences with determining where a given fraction falls in regards to "benchmark" fractions and will practice placing fractions on a number line.

Type: Lesson Plan

Equivalent Fractions: It Means the Same:

In this lesson, students will use models to represent equivalent fractions, including fractions greater than 1, and be able to identify representations of equivalence.

Type: Lesson Plan

Comparing and Placing Unit Fractions on a Number Line:

In this lesson, 3rd grade students will discover the value of fractions with a numerator of 1. The students will be able to compare the fractions and be able to correctly place them on a number line.

Type: Lesson Plan

Equivalent Fraction Dominoes:

Students will identify equivalent fractions to 1/2 using manipulatives and determine what happened to the numerator and denominator when an equivalent fraction was formed.  They will practice this idea by identifying equivalent fractions in a domino game.

Type: Lesson Plan

Fraction Measuring With Cuisenaire Rods:

In this lesson students will use Cuisenaire rods to measure distances of different lengths.They will also use and compare fractional amounts to find different ways of naming equivalencies.

Type: Lesson Plan

Twizzle the Fractions!:

In this food-themed lesson students work to understand why fraction comparisons must refer to the same whole to be valid. This lesson covers part "d" of standard MAFS.3.N.F.1.3. (In this standard there are parts a, b,and c.)

Type: Lesson Plan

## Lesson Study Resource Kit

Number and Operations - Fractions Lesson Study Resource Kit – Third Grade:

This lesson study resource kit can be used to guide and support teams of third grade teachers as they engage in lesson study focused on the academic standards in the Number and Operations - Fractions domain.

Type: Lesson Study Resource Kit

## Model Eliciting Activity (MEA) STEM Lesson

Physical Science Unit: Properties Lesson 22 Model Eliciting Activity: Animal Meal Planning:

In this MEA, students will have the opportunity to apply what they learned about physical properties to a realistic problem. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food. In the optional twist, students will need to modify their original diet for a senior chimpanzee.

This is a lesson in the Grade 3 Physical Science Unit on Properties. This is a themed unit of SaM-1's adventures at the CPALMS Rehabilitation and Conservation Center.  To see all the lessons in the unit please visit https://www.cpalms.org/page818.aspx .

Type: Model Eliciting Activity (MEA) STEM Lesson

## Original Student Tutorials

Lesson 22 Video: MEA Animal Meal Planning Part 2:

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA). In the optional twist, students will need to modify their original diet for a senior chimpanzee. The first video provided meal planning information to add to the knowledge students gained throughout the unit to start the challenge.

Type: Original Student Tutorial

Lesson 22 Video: MEA Animal Meal Planning:

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout the unit. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food.

In the optional twist, students will need to modify their original diet for a senior chimpanzee. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

Equal Fractions in Disguise:

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

Type: Original Student Tutorial

Fraction Comparisons With Pictures, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with the Same Numerators, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with the Same Denominator, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with a Different Whole:

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Comparing Fractions:

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Jon and Charlie's Run:

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Ordering Fractions:

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Equivalent Fractions Pointer:

In this activity, students highlight portions of circles or squares that are equivalent to a given fraction. As the student highlights sections, a pointer on a number line between zero and one updates so they can see when they are close or equal to the given fraction. This activity allows students to explore equivalent fractions by making it necessary that each of the three fractions have a different denominator but have the fractions be equal. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Teaching Idea

Fraction Action:

By making popcorn together with your child you may also introduce the concept of fractions.

Type: Teaching Idea

## Tutorials

Comparing Fractions on a Number Line and with Rectangular Models:

In this Khan Academy video four fractions are compared by plotting them on a number line and drawing models.

Type: Tutorial

Different Ways to Represent 1 as a Fraction:

Use fraction models and a number line to represent 1 as a fraction.

Type: Tutorial

## Virtual Manipulatives

Fractions Introduction:

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

Build a Fraction:

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

• Build equivalent fractions using numbers and pictures.
• Compare fractions using numbers and patterns
• Recognize equivalent simplified and unsimplified fractions

Type: Virtual Manipulative

Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

• Match fractions using numbers and pictures
• make the same fractions using different numbers
• Match fractions in different picture patterns
• Compare fractions using numbers and patterns

Type: Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

Fraction Models:

An interactive tool to represent a fraction circle, rectangle, or set model with numerators and denominators ranging from 1 to 100. The decimal and percent equivalents of the created fraction are also displayed.

Type: Virtual Manipulative

## MFAS Formative Assessments

Comparing Fractions:

Students compare two pairs of fractions and record their comparisons using the less than or greater than symbols.

Equivalent Fractions:

Students determine whether or not fractions are equivalent.

Four Fourths:

Students are given a number line scaled by fourths and ask to label the notches.

Generating Equivalent Fractions:

Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.

How Many Fourths Are In Two Wholes?:

Students are asked to divide two rectangles into fourths and then to consider how many fourths the two wholes represent.

The Cake Problem:

Students compare two fractional parts of two different wholes.

## Original Student Tutorials Mathematics - Grades K-5

Equal Fractions in Disguise:

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Lesson 22 Video: MEA Animal Meal Planning Part 2:

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA). In the optional twist, students will need to modify their original diet for a senior chimpanzee. The first video provided meal planning information to add to the knowledge students gained throughout the unit to start the challenge.

Type: Original Student Tutorial

Lesson 22 Video: MEA Animal Meal Planning:

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout the unit. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food.

In the optional twist, students will need to modify their original diet for a senior chimpanzee. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

Equal Fractions in Disguise:

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

Type: Original Student Tutorial

## Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Fraction Comparisons With Pictures, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with the Same Numerators, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with the Same Denominator, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with a Different Whole:

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Comparing Fractions:

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Jon and Charlie's Run:

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Ordering Fractions:

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Equivalent Fractions Pointer:

In this activity, students highlight portions of circles or squares that are equivalent to a given fraction. As the student highlights sections, a pointer on a number line between zero and one updates so they can see when they are close or equal to the given fraction. This activity allows students to explore equivalent fractions by making it necessary that each of the three fractions have a different denominator but have the fractions be equal. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Comparing Fractions on a Number Line and with Rectangular Models:

In this Khan Academy video four fractions are compared by plotting them on a number line and drawing models.

Type: Tutorial

Different Ways to Represent 1 as a Fraction:

Use fraction models and a number line to represent 1 as a fraction.

Type: Tutorial

## Virtual Manipulatives

Fractions Introduction:

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

Build a Fraction:

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

• Build equivalent fractions using numbers and pictures.
• Compare fractions using numbers and patterns
• Recognize equivalent simplified and unsimplified fractions

Type: Virtual Manipulative

Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

• Match fractions using numbers and pictures
• make the same fractions using different numbers
• Match fractions in different picture patterns
• Compare fractions using numbers and patterns

Type: Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

## Image/Photograph

Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

Fraction Comparisons With Pictures, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with the Same Numerators, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with the Same Denominator, Assessment Variation:

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Comparing Fractions with a Different Whole:

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Comparing Fractions:

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Jon and Charlie's Run:

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Ordering Fractions:

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

## Teaching Idea

Fraction Action:

By making popcorn together with your child you may also introduce the concept of fractions.

Type: Teaching Idea

## Virtual Manipulatives

Fractions Introduction:

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

Build a Fraction:

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

• Build equivalent fractions using numbers and pictures.
• Compare fractions using numbers and patterns
• Recognize equivalent simplified and unsimplified fractions

Type: Virtual Manipulative

Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

• Match fractions using numbers and pictures
• make the same fractions using different numbers
• Match fractions in different picture patterns
• Compare fractions using numbers and patterns

Type: Virtual Manipulative